A New Global Asymptotic Stability of Cellular Neural Network with Time-Varying Discrete and Distributed Delays

2012 ◽  
pp. 361-368
Author(s):  
Lin Zhu
Keyword(s):  
Neural Network ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Cellular Neural Network ◽  
Distributed Delays ◽  
Time Varying

ON THE GLOBAL ASYMPTOTIC STABILITY ANALYSIS OF DELAYED NEURAL NETWORKS

2005 ◽  
Vol 15 (12) ◽  
pp. 4019-4025 ◽  
Author(s):  
ZHAOHUI YUAN ◽  
DEWEN HU ◽  
LIHONG HUANG ◽  
GUOHUA DONG
Keyword(s):  
Neural Network ◽  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Hopfield Neural Network ◽  
Cellular Neural Network ◽  
Functional Method ◽  
Activation Functions ◽  
Delayed Neural Networks ◽  
System Parameters ◽  
Lyapunov Functional Method

In this paper, the problem of the global asymptotic stability (GAS) of a class of delayed neural network is investigated. Under the generalization of dropping the boundedness and differentiability hypotheses for activation functions, using some existing results for the existence and uniqueness of the equilibrium point, we obtain a couple of general results concerning GAS by means of Lyapunov functional method without the assumption of symmetry of interconnection matrix. Our results improve and extend some previous works of other researchers. Moreover, our conditions are presented in terms of system parameters, which have leading significance in designs and applications of GAS for Hopfield neural network (HNNs) and delayed cellular neural network (DCNNs).

Stabilization of Nonlinear Strict-Feedback Systems With Time-Varying Delayed Integrators

2011 ◽  
Author(s):  
Nikolaos Bekiaris-Liberis ◽  
Miroslav Krstic
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Closed Loop ◽  
Loop System ◽  
Time Varying ◽  
Feedback Systems ◽  
Closed Loop System ◽  
Feedback Form ◽  
Globally Asymptotically Stable ◽  
Strict Feedback

We consider nonlinear systems in the strict-feedback form with simultaneous time-varying input and state delays, for which we design a predictor-based feedback controller. Our design is based on time-varying, infinite-dimensional backstepping transformations that we introduce, to convert the system to a globally asymptotically stable system. The solutions of the closed-loop system in the transformed variables can be found explicitly, which allows us to establish its global asymptotic stability. Based on the invertibility of the backstepping transformation, we prove global asymptotic stability of the closed-loop system in the original variables. Our design is illustrated by a numerical example.

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